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On a Poisson's equation arising from magnetism

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  • We review the proof of existence and uniqueness of the Poisson's equation $\Delta u + {\rm div}\,{\bf m}=0$ whenever ${\bf m}$ is a unit $L^2$-vector field on $\mathbb R^3$ with compact support; by standard linear potential theory we deduce also the $H^1$-regularity of the unique weak solution.
    Mathematics Subject Classification: Primary: 35J05; Secondary: 3101.


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